Generally, in a wireless communications system, the communications system's capacity may be significantly improved when a transmitter (also referred to as a base station (BS)) has full or partial knowledge of a channel over which it will be transmitting. Information related to the channel may be referred to as channel state information (CSI). CSI may be obtained by the transmitter over a reverse feedback channel. A receiver (also referred to as a mobile station (MS)) of transmissions made by the transmitter may transmit CSI back to the transmitter over the reverse feedback channel. The receiver may estimate the channel, generate the CSI, and feed the CSI back to the transmitter.
However, since CSI feedback consumes communications system bandwidth, there is a desire to minimize the amount of information being feedback to the transmitter. Reducing the amount of information being feedback may involve the use of techniques such as compression, quantization using codebooks, partial information feedback, and so forth.
Channel information may be in the form of instantaneous channel feedback information, such as, codebook based limited rate feedback, or statistical channel information, such as, channel mean, channel correlation matrix, and so forth. Channel information is typically feedback from the receiver to the transmitter.
Transmit precoding/beamforming with limited feedback has been studied extensively and demonstrates significant performance gain in single user multiple input, multiple output (SU-MIMO). In general, a precoding codebook needs to be designed and maintained at both transmitter and receiver to facilitate the operation of limited feedback transmit precoding. The precoding codebook may be a collection of candidate precoding matrices and vectors and may serve as a common dictionary of current channel conditions to the transmitter and receiver.
It has been realized that codebooks should be designed to match the underlying channel characteristics. For example, for SU-MIMO independent identically distributed (iid) Rayleigh fading channels, Grassmannian line/subspace packing (GLP) based codebook has been shown to achieve near optimal performance. On the other hand, those GLP codebooks perform not so well under spatially correlated fading channels, wherein other codebooks have been shown to be relatively more robust, e.g., discrete Fourier transform (DFT) based codebooks and Householder based codebooks, among others. Other examples of codebooks may be complex Hadamard transform (CHT) based codebooks.